Square in a Circle

 

A square is kept inside a circle. It keeps expanding until all four of its vertices touch the circumference of the circle. Another smaller circle is kept inside the square now and it keeps expanding until its circumference touches all four sides of the square. The outer and the inner circle form a ring. Find the area of this ring.

Input

Input consists of multiple test cases.
Each test case contains one integer denoting the side-length of the square between the two circles.

Output

Print the area of the ring.

Sample Input 0

3

3

4

5

Sample Output 0

7.068583

12.566371

19.634954

 

Code:

import math

t=int(input())

while(t!=0):

    t-=1

    q=int(input())

    a_o=q/math.sqrt(2)

    a_i=q/2

    print("%.6f"%(math.acos(-1)*(a_o*a_o - a_i*a_i)))

   

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